Digital transmission over telephone channels may suffer from intersymbol interference (ISI) because of serious distortion in the available bandwidth. One approach to solve this problem is the use of adaptive equalizers. In this paper, a new design for adaptive equalizers is proposed, in which the computational complexity involved is significantly less than that of conventional adaptive equalizers because almost all the multiplication operations involved in the latter are replaced by addition operations in the former. The key point is that by taking intermediate decisions from the received signal and using these decisions with finite possible values, rather than received signal samples to calculate the equalized signal and to adjust the equalizer tap coefficients, multiplications can effectively be replaced by additions.